$TITLE  A FARMING PROBLEM (FARMING,SEQ=1)
$OFFUPPER
* This problem finds an optimal farming strategy.
*
*  References: 
*              Katta Murty,  Operations Research
*              Prentice Hall, 1995
*              Chapter 2-10.
*

  SETS
       CROPS   / wheat, corn /
       ANIMS /pigs, chickens/
       CTYPES grains are bought or sold /buy, sell/
   ANIMUSAGE /wheatbt, wheatsold, cornbt, cornsold, floor, hours, price/
       ANIMTYPES 
          /pigswtby
           pigswtsl
           pigscnby
           pigscnsl
           chickswtby
           chickswtsl
           chickscnby
           chickscnsl/
         USAGESELL(animusage)
          / wheatsold
           cornsold/;



PARAMETER
*** data for the crops
         YIELD(CROPS)  bushels per acre per year
           /wheat 55
            corn 95 /
         
         HOURS(CROPS)  manhours per bushel
           /wheat .15
            corn .70 /

         SELLPRICE(CROPS)  selling price per bushel
           /wheat 1.75
            corn .95 /

         BUYPRICE(CROPS)  buying price per bushel
           /wheat 2.50
            corn 1.50 /;

SCALAR
  AREATOT  acres for growing  /120/
  CULT  manhours for cultivation per acre per year /4/;

   TABLE    RES(animtypes,animusage)  
                     wheatbt   wheatsold   cornbt   cornsold floor hours price
pigswtby                25         0        0         0      25    25    200 
pigswtsl                 0        25        0         0      25    25    200 
pigscnby                 0         0       20         0      25    25    200 
pigscnsl                 0         0        0        20      25    25    200 
chickswtby              10         0        0         0      15    40    200 
chickswtsl               0        10        0         0      15    40    200 
chickscnby               0         0       25         0      15    40    200 
chickscnsl               0         0        0        25      15    40    200;


     

  SCALAR
     AREAF square feet for raising animals /10000/
     HOURSf hours available for raising animals /2000/;


 SCALAR
   HOURSTOT  total manhours available for the farmer /4000/
   HIRERATE  additional labour cost per hour       /4/;

  VARIABLES
       Z       total profit;

  POSITIVE VARIABLE 
             ACRES(crops)   acres devoted for each crop
             NUMBER(animtypes)  number of animals raised of each type
             BUY(crops)  bushels of each crop bought for animals
             EAT(crops) bushels of each crop eaten by animals
             HIRING     number of hours of hired labour for animals ;


  EQUATIONS 
       PROFIT        define objective function
       LABOUR   limit of total labour hours
       LABOUR1  limit of farmer labour hours
       LABOUR2  limit of total crop labour hours
       RAISE   square foot limit for raising animals
       FOOD    amount of bushels of farmer's grain used for animals
       GROW   acre limit for growing crops;

  PROFIT ..  Z  =E=  
   SUM(crops, (ACRES(crops)*YIELD(crops)-EAT(crops))*SELLPRICE(crops))  
       +SUM(animtypes, NUMBER(animtypes)*RES(animtypes,"price") )
             - SUM(crops, BUY(crops)*BUYPRICE(crops) )
               - HIRING*HIRERATE;

  LABOUR .. sum(crops, yield(crops)*hours(crops)*acres(crops) ) 
           + sum(animtypes, RES(animtypes,"hours")*number(animtypes)) 
                          =L= (HOURSTOT-HIRING*.1) + HIRING; 

  LABOUR1 .. HOURSTOT-HIRING*.1 =G= 0;

  LABOUR2 .. sum(crops, yield(crops)*hours(crops)*acres(crops) ) =L=
                   (HOURSTOT/2 - HIRING*.1) + HIRING;

  RAISE ..  SUM(animtypes, RES(animtypes,"floor")*number(animtypes))
                                =L=AREAF;

  FOOD .. SUM((animtypes,usagesell),  
            RES(animtypes,usagesell)*number(animtypes) )
                     =L= SUM(crops, ACRES(crops)*YIELD(crops) )  ;


  GROW ..   SUM(crops, acres(crops) ) =L= AREATOT ;




  MODEL FARMING /ALL/ ;

  SOLVE FARMING  USING LP MAXIMIZING Z ;

  DISPLAY grow.l, grow.m, number.l, number.m